P9-2004-218 П. Г. Акишин, А. В. Бутенко, А. Д. Коваленко, В. А

P9-2004-218
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‘µµ¡Ð¥´¨¥ ¡Ñ¥¤¨´¥´´µ£µ ¨´¸É¨ÉÊÉ Ö¤¥·´ÒÌ ¨¸¸²¥¤µ¢ ´¨°. „Ê¡´ , 2004
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Akishin P. G. et al.
Mathematical Simulation of the Magnetic Field End Effects
in Superconducting Nuclotron-Type Dipole Magnet
P9-2004-218
Mathematical model of a superconducting window-frame Nuclotron-type dipole
was developed within the frames of volume integral equations. 3D distributions
of the magnetic ˇeld in the magnet aperture were calculated for different operating
currents. The inuence of the magnet ferromagnetic yoke end proˇle (Rogovskytype) on the ˇeld nonlinearity is analyzed.
The investigation has been performed at the Veksler and Baldin Laboratory of
of High Energies and Laboratory of Information Technologies, JINR.
Communication of the Joint Institute for Nuclear Research. Dubna, 2004
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1. Œ’…Œ’ˆ—…‘ŠŸ ”Œ“‹ˆ‚Š ‹…Œ›
¸¸³µÉ·¨³ § ¤ ÎÊ ´ ̵¦¤¥´¨Ö · ¸¶·¥¤¥²¥´¨Ö ³ £´¨É´µ£µ ¶µ²Ö, ¸µ§¤ ¢ ¥³µ£µ ¸É ͨµ´ ·´Ò³¨ ɵ± ³¨ ¢ ³ £´¨É´ÒÌ ¸¨¸É¥³ Ì ¸ ¨§µÉ·µ¶´Ò³ Ë¥··µ³ £´¨É´Ò³ ³ É¥·¨ ²µ³. ʸÉÓ B(a), H(a), M(a) ¥¸ÉÓ ¨´¤Ê±Í¨Ö, ´ ¶·Ö¦¥´´µ¸ÉÓ
¨ ´ ³ £´¨Î¥´´µ¸ÉÓ ³ £´¨É´µ£µ ¶µ²Ö ¢ ɵα¥ a. ‚ µÉ¸Êɸɢ¨¥ ¶µ¢¥·Ì´µ¸É´ÒÌ
1
ɵ±µ¢ ¨ ɵ±µ¢, ¶·µÉ¥± ÕÐ¨Ì ¶µ Ë¥··µ³ £´¥É¨±Ê, ¢¥²¨Î¨´Ò B, H ʤµ¢²¥É¢µ·ÖÕÉ Ê· ¢´¥´¨Ö³ Œ ±¸¢¥²² :
rota (H(a)) = JS (a),
diva (B(a)) = 0,
lim |B(a)| = 0,
|a|→∞
(1)
£¤¥ JS Å ¢¥±Éµ· µ¡Ñ¥³´µ° ¶²µÉ´µ¸É¨ ɵ± (µÉ²¨Î¥´ µÉ ´Ê²Ö ɵ²Ó±µ ¢ µ¡³µÉ± Ì ³ £´¨É ). ‚¥²¨Î¨´Ò B, H, M ¸¢Ö§ ´Ò ¸²¥¤ÊÕШ³¨ ´¥²¨´¥°´Ò³¨
¸µµÉ´µÏ¥´¨Ö³¨:
H(a) =
B(a)
,
µ (|B(a)|) µ0
M(a) =
B(a)
− H(a),
µ0
(2)
£¤¥ µ0 Å ¡¸µ²ÕÉ´ Ö ³ £´¨É´ Ö ¶·µ´¨Í ¥³µ¸ÉÓ ¢ ±Êʳ , µ(x) Å ³ £´¨É´ Ö
¶·µ´¨Í ¥³µ¸ÉÓ (¢´¥ ¦¥²¥§´µ£µ Ö·³ ɵ¦¤¥¸É¢¥´´µ · ¢´ Ö ¥¤¨´¨Í¥, ¢´ÊÉ·¨
¦¥²¥§´µ£µ Ö·³ Å ´¥²¨´¥°´ Ö ËÊ´±Í¨Ö, Ì · ±É¥·¨§ÊÕÐ Ö ¸¢Ö§Ó ³¥¦¤Ê H
¨ B ¤²Ö ¤ ´´µ£µ ɨ¶ Ë¥··µ³ £´¥É¨± ). £· ´¨Í¥ · §¤¥² ¸·¥¤ ¸ · §²¨Î´Ò³¨ ³ £´¨É´Ò³¨ Ì · ±É¥·¨¸É¨± ³¨ ¢Ò¶µ²´ÖÕÉ¸Ö Ê¸²µ¢¨Ö ´¥¶·¥·Ò¢´µ¸É¨
´µ·³ ²Ó´µ° ¨ É ´£¥´Í¨ ²Ó´µ° ¸µ¸É ¢²ÖÕÐ¨Ì ¢¥±Éµ·µ¢ H ¨ B ¸µµÉ¢¥É¸É¢¥´´µ:
(n, (B2 − B1 )) = 0,
[n × (H2 − H1 )] = 0,
(3)
£¤¥ n Å ¥¤¨´¨Î´Ò° ¢¥±Éµ· ´µ·³ ²¨ ± ¶µ¢¥·Ì´µ¸É¨ · §¤¥² ¸·¥¤.
“· ¢´¥´¨Ö (1)Ä(3) ´¥Ê¤µ¡´Ò ¤²Ö ´¥¶µ¸·¥¤¸É¢¥´´µ£µ ´ ̵¦¤¥´¨Ö ¢¥±Éµ·ËÊ´±Í¨° H(a), B(a). ‘ÊÐ¥¸É¢Ê¥É ¡µ²Óϵ¥ Ψ¸²µ ¶µ¸É ´µ¢µ±, ¢ÒÉ¥± ÕШÌ
¨§ Ê· ¢´¥´¨° Œ ±¸¢¥²² [5]. ‚ ¤ ´´µ° · ¡µÉ¥ ¨¸¶µ²Ó§Ê¥É¸Ö ¨´É¥£· ²Ó´ Ö
¶µ¸É ´µ¢± § ¤ Ψ ³ £´¨Éµ¸É ɨ±¨ [6]:
1
1
H(a) = HS (a) +
∇a
(4)
M(x), ∇a
dνx ,
4π
|x − a|
Ω
£¤¥ H ¨ M ʤµ¢²¥É¢µ·ÖÕÉ ´¥²¨´¥°´Ò³ ¸µµÉ´µÏ¥´¨Ö³ (2).
„²Ö ¤¨¸±·¥É¨§ ͨ¨ ´¥²¨´¥°´ÒÌ µ¡Ñ¥³´ÒÌ ¨´É¥£· ²Ó´ÒÌ Ê· ¢´¥´¨° ¶·¥¤² £ ¥É¸Ö ¨¸¶µ²Ó§µ¢ ÉÓ ³¥Éµ¤ ±µ²²µ± ͨ¨. ‘²¥¤ÊÖ [7], · §µ¡Ó¥³ µ¡² ¸ÉÓ Ω,
§ ¶µ²´¥´´ÊÕ Ë¥··µ³ £´¥É¨±µ³, ´ ¶µ¤³´µ¦¥¸É¢ {Ωl }:
Ω=
N
Ωl .
l=1
Œ¥· ¶¥·¥¸¥Î¥´¨Ö Ωl c Ωm · ¢´ ´Ê²Õ ¶·¨ l = m. ‚ ± ¦¤µ³ Ωl ¢ ± Î¥¸É¢¥
ɵα¨ ´ ¡²Õ¤¥´¨Ö al ¢Ò¡¥·¥³ Í¥´É·µ¨¤ Ωl :
xdνx
Ωi
.
al = dνx
Ωl
2
·¨¡²¨§¨³ ´ ³ £´¨Î¥´´µ¸ÉÓ M(x) ¢ ± ¦¤µ³ Ô²¥³¥´É¥ Ωi ¶µ¸ÉµÖ´´Ò³ ¢¥±Éµ·µ³ Mi .
’µ£¤ ¤¨¸±·¥É¨§µ¢ ´´ Ö ¸¨¸É¥³ Ê· ¢´¥´¨° (4) ¨³¥¥É ¸²¥¤ÊÕШ° ¢¨¤:


N
∇a 
1

S
Hl = H (al ) +
dν
M
,
∇
,
(5)

j
a
x 
4π
|x − a|
j=1
Ωj
a=al

1
HS (al ) = rota 
4π
ΩS

J(x)

dνx |x − a|
.
(6)
a=al
‚¥±Éµ·Ò Hl ¨ Ml ʤµ¢²¥É¢µ·ÖÕÉ ´¥²¨´¥°´Ò³ ¸µµÉ´µÏ¥´¨Ö³ (2).
‚¢¥¤¥³ ¸²¥¤ÊÕШ¥ µ¡µ§´ Î¥´¨Ö. ʸÉÓ
B̂ = (B1 , B2 , ..., BN )T , M̂(B̂) = (M(B1 ), M(B2 ), ..., M(BN ))T ,
ĤS = (HS (a1 ), HS (a2 ), ..., HS (aN ))T .
¶·¥¤¥²¨³ ³ É·¨ÍÊ [A] ¸²¥¤ÊÕШ³ µ¡· §µ³:


[A11 ] ... [A1N ]
...
...  ,
[A] =  ...
[AN 1 ] ... [AN N ]
£¤¥ [Aij ] Å ³ É·¨Í · §³¥·´µ¸É¨ [3 × 3], É ± Ö, Îɵ ¤²Ö ²Õ¡µ£µ ¶µ¸ÉµÖ´´µ£µ
¢¥±Éµ· M ¸¶· ¢¥¤²¨¢µ ¸µµÉ´µÏ¥´¨¥


∇a 
1

M, ∇a
[Aij ] M =
.
dνx 

4π
|x − a|
Ωj
a=ai
“ΨÉÒ¢ Ö (2), ¸¨¸É¥³Ê (5) ³µ¦´µ § ¶¨¸ ÉÓ ¢ ¢¨¤¥
B̂ = µ0 ĤS + ([A] + [E]) M̂(B̂),
(7)
£¤¥ [E] Å ¥¤¨´¨Î´ Ö ³ É·¨Í · §³¥·´µ¸É¨ [3N × 3N ].
„²Ö ·¥Ï¥´¨Ö ¸¨¸É¥³Ò Ê· ¢´¥´¨° (7) ¶·¨³¥´Ö¥É¸Ö ¸²¥¤ÊÕШ° ¨É¥· ͨµ´´Ò° ¶·µÍ¥¸¸:
B̂k+1 = µ0 ĤS + ([A] + [E]) M̂(B̂k+1 ),
(8)
B̂0 = µ0 ĤS , k = 0, 1, 2, ...
3
(9)
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³ £´¨É .
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¶·µË¨²Ö µ£µ¢¸±µ£µ
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¶¥·¥¸Î¥É ¶µ²Ö ¤²Ö µ¤´µ£µ §´ Î¥´¨Ö
ɵ± ¢ µ¡³µÉ± Ì ¸µ¸É ¢¨²µ µ±µ²µ
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‚¢¨¤Ê ¸²µ¦´µ¸É¨ ¶µ¢¥¤¥´¨Ö ¶µ²Ö
´ ±· Õ ³ £´¨É ¤²Ö ¶µ²ÊÎ¥´¨Ö ·¥Ï¥´¨Ö ´¥²¨´¥°´µ° ¸¨¸É¥³Ò (7) ¢
Ôɵ³ ¸²ÊÎ ¥ ¶µÉ·¥¡µ¢ ²µ¸Ó µ±µ²µ
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2 ¨ 2,5 ¸³ ¶·¨ §´ Î¥´¨¨ ¶µ²Ö ¢ Í¥´É·¥ ³ £´¨É 2 ’² ¶·¨¢¥¤¥´Ò ¢ É ¡²¨Í¥.
5
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(¸¶²µÏ´ Ö ²¨´¨Ö) ¶·¨ §´ Î¥´¨ÖÌ Éµ±µ¢ ¢ µ¡³µÉ± Ì ¢µ§¡Ê¦¤¥´¨Ö: a, ¢ Å 1,2 ± (¶µ²¥
0,42 ’²); ¡, £ Å 6,1 ± (¶µ²¥ 2 ’²)
ƒ¥µ³¥É·¨Ö
ƒ ·³µ´¨±a
ɵ·Í¥¢µ°
Î ¸É¨
B1 (R = 2 ¸³/2,5 ¸³) B3 (R = 2 ¸³/2,5 ¸³)
B5 (R = 2 ¸³/2,5 ¸³)
¡ÒδҰ
¶µ²Õ¸
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1. ‘³¨·´µ¢ . ., Šµ¢ ²¥´±µ . „. ʱ²µÉ·µ´ Å ¸¢¥·Ì¶·µ¢µ¤ÖШ° ʸ±µ·¨É¥²Ó Ö¤¥· ¢
‹‚ ˆŸˆ (¸µ§¤ ´¨¥, · ¡µÉ ¨ · §¢¨É¨¥) // ¨¸Ó³ ¢ —Ÿ. 2004. ’. 1, º 6(123).
‘. 11Ä40.
2. Moritz G. et al. Towards Fast Pulsed Superconducting Synchrotron Magnets // Proc. of
PAC'2001, Chicago, June 2001. P. 211Ä214.
3. Kovalenko A. et al. Optimization of a superferric Nuclotron-type dipole for the GSI
fast-pulsed synchrotron (presented at MT-17, Geneva, September 2001) // IEEE Trans.
on Appl. Superconductivity. 2002. V. 12, No. 1. P. 161Ä165.
4. Kovalenko A. D. et al. Progress in the design and study of a superferric dipole magnet
for the GSI fast-pulsed synchrotron SIS100 (MT-18, Morioka, Japan, October 2003) //
IEEE Trans. on Applied Superconductivity. 2004. V. 14, No. 2. P. 321Ä324.
5. °·Ö´ . ., †¨¤±µ¢ …. ., ”¥¤µ·µ¢ . ‚. ¨ ¤·. —¨¸²¥´´Ò¥ ²£µ·¨É³Ò · ¸Î¥É ³ £´¨É´ÒÌ ¸¨¸É¥³ ¢ ʸ±µ·¨É¥²ÖÌ § ·Ö¦¥´´ÒÌ Î ¸É¨Í // —Ÿ. 1990. T. 21, ¢Ò¶. 1.
C. 231Ä307.
6. Newman M. J., Trowbridge G. W., Turner L. R. GFUN: An interactive program as aid to
magnet design // Proc. 4th Intern. Conf. Magnet Technol. Brookhaven, 1972. P. 617Ä
626.
7. ±¨Ï¨´ . ƒ. ¡ µ¤´µ³ ³¥Éµ¤¥ · ¸Î¥É ³ £´¨É´ÒÌ ¶µ²¥° ¢ ¸¨¸É¥³ Ì ¸ µ¸¥¸¨³³¥É·¨Î´µ° ±µ´Ë¨£Ê· ͨ¥° Ë¥··µ³ £´¥É¨± // †‚Œ ¨ Œ”. 1989. T. 29. C. 1168Ä1174.
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